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Reviewing Universal Mathematics Instruction Session 2
Facilitators: Heidi Erstad & Sharmaé Roberts
The Wisconsin RtI Center/Wisconsin PBIS Network (CFDA #84.027) acknowledges the support of the Wisconsin Department of Public Instruction in the development of this training and for the continued support of this federally-funded grant program. There are no copyright restrictions on this document; however, please credit the Wisconsin DPI and support of federal funds when copying all or part of this material.
www.wisconsinrticenter.org/math-tr
All presentation materials and additional resources can be found at:
Outcomes and Objectives • Understand what is required of the
Wisconsin Standards for Mathematics
• Understand the key components of Guiding Principles for Teaching and Learning in a mathematics classroom
• Outline K-12 to gauge your district’s current implementation of systemic universal mathematics
• Improve universal level mathematics in your district
Facilitator Time Keeper
Recorder Spokesperson
Team Roles
Notice moments of discomfort and stay
curious
Listen fully, with your ears, eyes and heart
Speak your truth without blame or
judgment
Be open to the experience and each
other
Can we commit to…
Source: National Equity Project
Agreements
1. Review work from day 1
2. Review and outline Wisconsin’s Guiding Principles 1, 2, 3, 4 for Teaching and Learning Math
Day 2
2
Today: What are we compelled to do in order to provide for students in light of Day 1 concepts?
2
Overview of MLSS and Importance of Universal
REVIEWING THE CONTENT OF DAY 1
What was one big idea you learned about your school from yesterday’s session? About your team?
Data: Identifying the Need
Collaboration and Screening
Design Principles: Focus, Rigor & Coherence
Standards for Mathematical Practice
High quality standards are necessary for effective teaching and learning, but insufficient
Standards do not describe or prescribe the essential conditions required to make sure mathematics works for all students
Wisconsin’s Guiding Principles for Teaching and Learning
1. Every student has the right to learn.
2. Instruction must be rigorous and relevant.
3. Purposeful assessment drives instruction and affects learning.
4. Learning is a collaborative responsibility.
5. Students bring strengths and experiences to learning.
6. Responsive environments engage learners.
http://dpi.wi.gov/standards/guiding-principles.html
1. Every student has the right to learn significant mathematics.
2. Mathematics instruction must be rigorous and relevant.
3. Purposeful assessment drives mathematics instruction and affects learning.
4. Learning mathematics is a collaborative responsibility.
5. Students bring strengths and experiences to mathematics learning.
6. Responsive environments engage mathematics learners.
HANDOUT 2.1
Wisconsin Guiding Principles for Teaching and Learning Mathematics
• Our school embraces an RtI vision centered on achieving high levels of academic and behavioral success for all students in mathematics.
• We differentiate universal mathematics curriculum and instruction based on student needs.
• We use research-based practices and/or programs within our universal mathematics curriculum and instruction.
• We provide universal curriculum and instruction that engages students
• We provide universal mathematics curriculum and instruction that use the cultural beliefs, practices and experiences of our students
• We use a process to ensure that our universal mathematics curriculum and instruction are delivered with fidelity (i.e. as intended).
SIR Alignment with Principles
Mathematical proficiency is essential for every student in
Wisconsin. Students need to be able to formulate, represent,
and solve problems; explain and justify solutions and solution
paths; and see mathematics as sensible, useful, and
worthwhile. In order to achieve this vision, all students must
have access to challenging, rigorous, and meaningful
mathematics. Schools and classrooms need to be organized
to convey the message that all students can learn
mathematics and should be expected to achieve.
1. Every student has the right to learn significant mathematics.
Wisconsin Guiding Principles for Teaching and Learning Mathematics
3
Principle: Access and Equity
“An excellent mathematics program requires that all students have access to high-quality mathematics curriculum, effective teaching and learning, high expectations, and the support and resources needed to maximize their learning potential.”
Wisconsin Guiding Principles for Teaching and Learning Mathematics
1. Every student has the right to learn significant mathematics.
2. Mathematics instruction must be rigorous and relevant.
3. Purposeful assessment drives mathematics instruction and
affects learning.
4. Learning mathematics is a collaborative responsibility.
5. Students bring strengths and experiences to mathematics
learning.
6. Responsive environments engage mathematics learners.DPI. Wisconsin Guiding Principles for Teaching and Learning: What Do They Look Like in Mathematics Classrooms?
All means all
What is it about our educational system that is reinforcing differential
outcomes or failing to eliminate them?
Throughout this section, keep in mind students identified on Day 1
not yet well-served by your system…
Turn on your internal deflection checker!
Adapted from NYU Steinhardt Identifying the Root Causes of Disproportionality
Access, courses, teacher licensure, collaboration schedule, curriculum, grading, discipline, homework
Policies & ProceduresWhat’s written…
PracticesWhat’s done…
BeliefsWhat’s thought to be
true…
Instruction, tasks, assessment, collaboration, learning environment
Expectations, biases, mindsets, misconceptions, nature of conversations
…about math, teaching, learning, students, families
INEQUITIES IN MATH OUTCOMES
Let’s be clear: Teachers alone are not responsible for inequities in math outcomes - - either creating them or fixing them
Policies & ProceduresWhat’s written…
PracticesWhat’s done…
BeliefsWhat’s thought to be
true…
…about math, teaching, learning,
students, families
THE CAUSES OF INEQUITIES ARE COMPLEX
“School mathematics simultaneously serves as a gateway and gatekeeper for various opportunities in and out of school.”
“[Schools] play a crucial role in deciding which students will or will not have access to these opportunities.”
The Impact of Identity in K-8 Mathematics, p. 5
4
Dig Deeper
HANDOUT 2.2
Access and Equitypages 59 –
middle of 66
Different Resources, Different Results
pages 21 - 27
Instructional Materials
& Professional Learning (main page, video,
and research)
Jigsaw reading
Record DiscussShare 2-3 key take-aways that are relevant to your school
1
2 3
Principle: Access and Equity
“The question is not whether all students can succeed in mathematics, but whether the adults organizing mathematics learning opportunities can alter [existing policies,] beliefs and practices to promote success for all.” p. 61
An Equity StoryEliminating Disproportionality in AP classes
"When equity is not consciously addressed, inequality is often unconsciously replicated" http://act.colorlines.com/
1. Listen for same area of focus: POLICIES, PRACTICES, BELIEFS
2. Use side 2 to record
System Equity
Equality Equity
High SchoolEnrollment: 1507 students
26.4% Free/Reduced Lunch
0.5% 3.5%
9.8%
11.9%
0.2%
70.5%
3.6%
Amer Indian
Asian
Black
Hispanic
Pacific Isle
White
Two or More
Problem Analysis
Plan Implementation
Plan Evaluation
Problem Identification
5
Problem Identification
AP course enrollment, across all courses, predominantly White and Asian students and students not eligible for subsidized lunch
356
13 11
15 4
1
15 18
1612 18
2
2
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Med/highincome
Lowincome
Med/highincome
Lowincome
Med/highincome
Lowincome
Med/highincome
Lowincome
White & Asian Hispanic/Latino Black/AfricanAmerican
All Other Races
Students enrolled in AP Students to add to AP
60% participation 18% participation among all underrepresented students
Baseline
11th/12th grade AP participation by race and income
Close racial/economic participation gaps in AP courses by 70% by enrolling 125 underrepresented students by end of year 1
Close gaps completely (100%) by enrolling students in AP at racially /socio-economically proportionate rates by end of year 2
Through retention and support structures, ensure that 100% of all identified new AP students are still enrolled in and passing an AP course in November and May.
Goals
Problem Analysis
Plan Implementation
Plan Evaluation
Problem Identification
Problem Analysis
Staff listening groups and survey:
Beliefs about and expectations for students
Student survey:
Post-HS aspirationsBarriers to AP participation
Survey of Students’ Post-secondary Plans
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Advanced degree 4 year college 2 year associate
Med/high Income
LowIncome
Med/high Income
LowIncome
Med/high Income
LowIncome
Med/high Income
LowIncome
White/Asian Hispanic/Latino African-American Other race / ethnicity
6
Student-identified barriers to AP
Unaware of purpose/benefit of AP classes
“No one has ever talked to me about AP”*
Cost of materials and exam
Prerequisites (e.g. essays, summer reading)
Requirement to take exam
Afraid that low AP grade would lower GPA, make it harder to get into college
Don’t feel welcome
Gaps in Student/Teacher Perceptions
Staff Students
40% Believed that AP is “not a social norm for some students.”
95% Want to go to college
92% Report that their parents expect them to attend college
81%
Agreed with the statement: “We nurture the attitudes and dispositions that help students be successful in class and persevere through challenges.”
54% “I don’t think I can be successful/get a good grade”
68% Thought students would not enroll in AP because it would be too much work
38% Listed “too much work” as a factor for not enrolling
Student level
System level
Problem Analysis
Plan Implementation
Plan Evaluation
Problem Identification
Who have existing “readiness” indicators, but not enrolled
Who are just shy of all readiness indicators, with grit and post-secondary interest
Identified students…
Student level
STUDENT INSIGHT CARD 2014-15
Personalized Outreach with Data
Carlos
10th grader(on outreach list)
Carlos’ Educational Goal Advanced degree
Career interests Engineering, medical field
Trusted adults at school R. Dow, J. Bailey, M. Austin
Study skills support R. Dow
GPA 3.15
Subject interest Science
Indicators of AP Readiness
Willing to take AP
Demonstrated assets:• Community leadership• Growth mindset
AP Access Barriers
• No adult encouragement• Unsure how to enroll• Not sure how to get help• Doesn’t think he’s able to be successful/get a good grade• Worried that AP might hurt his GPA
Comments
I know that I can do a lot better in school. I just sometimes get lazy to do homework assignments or projects and I leave it for the last day before it’s due. I know I’m a really smart kid, but sometimes learning doesn’t click right away and the classes pressure you to get it right away and then take a test or quiz on it.
Student level
Purpose-Building and CommunicationStudent level
AP meeting for all, including college admissions counselor
Eliminated pre-requisites and AP exam requirement
Held AP parent night
7
Supports for enrolled students
Student level
Summer boot camp
Peer tutoring
A+ time
Study hall scheduled
with AP teacher
MORE supports for enrolled students
Student level
Paid for books and
tests for F/R lunch
students
Changed “drop” policy
Carefully clustered
students of color
Partnered with
community to run college
clubs
Purpose-building, professional development & support
Main concern expressed by staff:
“We’re setting kids up to fail”
Principal consistently challenged staff beliefs about potential of students: “So how can we set kids up to succeed?”
System level
Purpose-building, professional development & support
System level
Focus on relationship building & communal
classroom environment
Expanded teacher repertoire of instructional
strategies
Problem Analysis
Plan Implementation
Plan Evaluation
Problem Identification
Close racial/economic participation gaps in AP courses by 70% by enrolling 125 underrepresented students by end of year 1
Close gaps completely (100%) by enrolling students in AP at racially /socio-economically proportionate rates by end of year 2
Through retention and support structures, ensure that 100% of all identified new AP students are still enrolled in and passing an AP course in November and May.
Goals
8
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Med/high Income
LowIncome
Med/high Income
LowIncome
Med/high Income
LowIncome
Med/high Income
LowIncome
White/Asian Hispanic/Latino African-American Other race / ethnicity
Baseline Year 1 Year 2
Goal: Close gaps (100%) by enrolling students in AP at racially / socio-economically proportionate rates in 2 years.
11th/12th Grade AP participation by race and income Through retention and support structures, ensure that 100% of all identified new AP students are still enrolled in and passing an AP course in November and May.
Goals
Fall Year 1: 94% of all AP students and 83% of UR AP students still enrolled & passing.
Spring Year 2: 86% of UR AP students enrolled & passing.
Results
Other dimensions to overall equity work
Membership in external
equity networks
Ongoing equity leadership training
Alternative discipline structures
EQUITY as District priority
Student affinity groups
Student multi-cultural leadership council
“This is challenging work, but it’s important work and it’s
the right work to do.”
Principal
In round robin format, share one key take-away from this story for your school to think about.
Outline Principle 1
Pay particular attention to identifying strengths/areas for improvement that impact inequities in your data
Basic tracks; same course name but different expectations; separate SpEd classes; gatekeepers to advanced courses
Principle 1: Every student has the right to learn significant mathematics
Strengths Areas for Improvement
9
Section Outcomes
• Understand the importance of
mathematical tasks, Depth of
Knowledge, and productive struggle
within mathematical tasks.
• Analyze current local understanding and
use of rigorous tasks and productive
struggle
Teachers focus on engaging students in using mathematical reasoning,
making mathematical connections, and modeling and representing
mathematical ideas in a variety of ways. The mathematics curriculum
needs to integrate and sequence important mathematical ideas so that
mathematics makes sense. Teachers use rich tasks to engage students in
the development of conceptual understanding and procedural skills. An
emphasis on connections within mathematics helps students see
mathematics as a coherent and integrated whole rather than as a set of
isolated and disconnected skills and procedures. Through mathematical
applications, students recognize the usefulness of mathematics and
appreciate the need to study and understand mathematical skills and
concepts.
2. Mathematics instruction must be rigorous and relevant.
Wisconsin Guiding Principles for Teaching and Learning Mathematics
1. Every student has the right to learn significant mathematics.
2. Mathematics instruction must be rigorous and relevant.
3. Purposeful assessment drives mathematics instruction and
affects learning.
4. Learning mathematics is a collaborative responsibility.
5. Students bring strengths and experiences to mathematics le
6. Responsive environments engage mathematics learners.
Use rich tasks to engage students in the development of
conceptual understanding and procedural skills.
Through mathematical applications, students recognize the
usefulness of mathematics and appreciate the need to study
and understand mathematical skills and concepts.
Wisconsin Guiding Principles for Teaching and Learning Mathematics
Mathematical Tasks
Effective teaching of mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies.
Research on Mathematical Tasks
• All tasks do not provide the same opportunities for student thinking and learning.
• Student learning is greatest in classrooms where the tasks encourage high-level thinking and reasoning.
• Tasks with high cognitive demand are most difficult to implement well and are often transformed into less demanding tasks during instruction.
Self-reflection on Tasks and SMP
• Is the problem interesting and challenging to students?
• Does the problem involve meaningful mathematics?
• Does the problem give students an opportunity to apply and extend mathematics?
• Does the problem allow for multiple strategies or solutions?
Source: Kanold, T., et al (2012). Common Core Mathematics in a PLC at Work. Solution Tree.
10
Depth of Knowledge
Recall and Reproduction1
Skills and Concepts2
Short-term Strategic Thinking3
Extended Thinking4
HANDOUT
Complexity ≠ Difficulty
DOK refers to the kind of thinking required by a task.
Recall of a fact, information, or procedure. This requires eliciting information such as a fact, definition, term, or simple procedure, as well as performing a simple algorithm or applying a formula.
Key Words: identify, recall, recognize, use, and measure
Recall and Reproduction1
Includes the engagement of some mental processing beyond recalling or reproducing a response
Key Words: classify, organize, estimate, collect and display data, compare, explain, describe, or interpret
Skills and Concepts2 Lower-level Cognitive Tasks
Memorization Procedures without Connections
Producing previously learned facts
Algorithms
Have no connections to the concepts
Require limited cognitive demand
Rules or definitionscannot be solved using procedures
Focused on producing correct answers more than mathematical understanding
Require no explanations, or explanations that focus on describing the procedure
Requires reasoning, planning, using evidence, explaining an answer, and a higher level of thinking
Keywords: draw a conclusion, make a generalization, support with an argument, explain, solve a complex or non-routine problem
Short-term Strategic Thinking3
Requires complex reasoning, planning, developing, and thinking
Keywords: design and conduct, develop and carry out the project, create and prove conjectures, make connections between discoveries, critique plans and designs
Extended Thinking4
11
High-level Cognitive Tasks
Procedures with Connections
Doing Mathematical Tasks
Focus the students’ attention on the use of procedures
Require complex and non-algorithmic thinking
Usually represented in multiple ways
Require students to explore and understand the nature of mathematical concepts
Require some degree of cognitive effort
Require students to access relevant knowledge/experiences and use them appropriately to work through task
Require students to analyze tasks
As a table group, sort the mathematical tasks by their corresponding Depth of Knowledge.
• Recall and Reproduction
• Skills and Concepts
• Short-term Strategic Thinking
• Extended Thinking
Depth of Knowledge Sorting TaskActivity
Research on Mathematical Tasks
• All tasks do not provide the same opportunities for student thinking and learning.
• Student learning is greatest in classrooms where the tasks encourage high level thinking and reasoning.
• Tasks with high cognitive demand are most difficult to implement well and are often transformed into less demanding tasks during instruction.
Examine
Supporting Productive Struggle
As a group, determine the depth of knowledge called for in the Smartphone Plans task.
Read Fig 8. p. 23 PtA: A look inside two algebra classrooms
Discuss Ms. Carson and Ms. McDonald’s approachesWhat were the actions of each of the teachers? What depth of knowledge was expected of students as a result?
Algebra Task: Smartphone PlansYou are trying to decide which of two smartphone plans would be better. Plan A charges a basic fee of $30 per month and 10¢ per text message. Plan B charges a basic fee of $50 per month and 5¢ per text message.
How many text messages would you need to send per month for plan B to be the better option. Explain your decision. p. 20 PtA
Support Productive Struggle in Learning Mathematics
Teachers sometimes perceive student frustration or lack of immediate success as indicators that they have somehow failed their students. As a result, they jump in to ‘rescue’ students by breaking down the task and guiding students step-by-step through the difficulties. While well intentioned, this…deprives students of an opportunity to fully engage in making sense of mathematics.
Support Productive Struggle in Learning Mathematics
Struggle does not mean needless frustration or extreme levels of challenge. It means students expend some effort to make sense of mathematics. Unproductive struggle is a situation in which students make no progress towards sense making.
12
Factors that Impact the Degree of Rigor in the Mathematics Classroom
HANDOUT 2.3
Outline then analyze Principle 2
Teachers measure mathematical proficiency by using a variety of
purposeful assessments before, during, and after instruction. Rich
assessment tasks ask students to demonstrate their understanding by
representing mathematical situations, solving problems as developed
in the classroom, and justifying their solutions. Valuable assessments
provide both students and teachers with the opportunity to reflect on
students’ mathematical communication, precision, and reasoning.
Teachers use resulting data to adapt their instruction and the learning
environment so that all students will understand new mathematics
concepts and content.
3. Purposeful assessment drives mathematics instruction and affects learning.
Wisconsin Guiding Principles for Teaching and Learning Mathematics
1. Every student has the right to learn significant mathematics.
2. Mathematics instruction must be rigorous and relevant.
3. Purposeful assessment drives mathematics instruction and
affects learning.
4. Learning mathematics is a collaborative responsibility.
5. Students bring strengths and experiences to mathematics
learning.
6. Responsive environments engage mathematics learners.
Rich assessment tasks ask students to demonstrate their understanding
Provides both students and teachers with the opportunity to reflect on students’ mathematical communication, precision, and reasoning
Occurs before, during, and after instruction
Wisconsin Guiding Principles for Teaching and Learning Mathematics
Strategic Assessment SystemFORMATIVE INTERIM SUMMATIVE
PurposeTo quickly inform
instruction
To benchmark and monitor
progressTo evaluate learning
Data typeSpecific, immediate,
actionable feedback
Multiple data points across
timeCumulative snapshots
Nature of
assessment
Daily ongoing instructional
strategies
Periodic diagnostic /
Common assessmentsStandardized assessments
FocusStudent/Classroom-
centered
Grade-level/School-
centered
School /District/State-
centered
Answers the
question
What comes next for
learning? Is the instruction /
program effective?
What progress are students
making? Did the instruction
/ program work?
Are our students meeting
the standards? How
successful was the
instruction/program?
School/district examples formathematics ->
Adapted from Wisconsin Department of Public Instruction. (2015). Available http://dpi.wi.gov/strategic-assessment
Think systemic (across like classrooms/courses) and systematic( i.e. in your lesson plans)
13
Formative practices are designed to quickly inform instruction by
providing specific and immediate feedback through daily, ongoing
instructional strategies that are student- and classroom-centered,
and that answer, “What comes next for student learning?"
DPI Definition
Formative practices are used to adjust instruction and promote
ongoing reflection for BOTH students and teachers. This
deliberate process embedded within the
teaching and learning cycle has the power
to transform student learning and
improve student outcomes.
1. Engaging prior knowledge is required to create new learning
2. Experience and feedback are needed to move from novice to expert
3. Metacognitive approach to learning leads to increased student control and motivation to engage
Research Support
Which types of assessment(s) have biggest impact on student achievement?
Wiliam, D. (2007) What Does Research Say the Benefits of Formative Assessment Are? The National Council of Teachers of Mathematics
PracticeEffect Size
Student goal-setting 1.44
Formative assessment .90
Feedback .73
Meta-cognitive strategies
.69
Source: http://map.mathshell.org
Formative assessment
Pre-test
Post-test
Delayed test
Sco
res
Direct instruction
Pre-test
Post-test
Delayed test
Sco
res
MARS Mathematics Assessment Project (MAP)
14
HANDOUT 2.4
CCSS.MATH.CONTENT.HSG.CO.C.11
Prove theorems about parallelograms.
https://www.teachingchannel.org/videos/class-warm-up-routine?fd=1
CCSS.MATH.CONTENT.8.EE.C.7Solve linear equations in one variableCCSS.MATH.CONTENT.8.EE.C.7.BSolve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms..
Choose one of the formative assessment strategies shown: MyFavorite No or Is it a Parallelogram?
Discuss:How does the selected strategy connect with the DPI definition of Formative Assessment?
How would you use the information you gained from this assessment strategy to plan what might come next for student learning?
Team Talk about Formative Assessment Outline then analyze Principle 3
• Understand the importance of discourse in a mathematics classroom.
• Analyze current local understanding and use of discourse.
1. Every student has the right to learn significant mathematics.
2. Mathematics instruction must be rigorous and relevant.
3. Purposeful assessment drives mathematics instruction and
affects learning.
4. Learning mathematics is a collaborative responsibility.
5. Students bring strengths and experiences to mathematics
learning.
6. Responsive environments engage mathematics learners.
Purposeful interactions in the classroom.
Contexts and conditions for an interdependent learning environment
Opportunities for students to communicate
Wisconsin Guiding Principles for Teaching and Learning Mathematics
15
Importance of Discourse
Classroom discourse provides a supportive context
for students to share partial understandings and
misconceptions, and instructionally embedded
assessment allows teachers to gather information
about students’ partial understandings or
misconceptions and to further investigate students’
intended meaning through additional probing,
guiding and reframing of questions. Webb (2004)
Using Discourse to Increase Student Achievement
.82 Effect Size
HANDOUT 2.4
CCSS.MATH.CONTENT.HSG.CO.C.11
Prove theorems about parallelograms.Why Use Talk in Math Classrooms?
• Clarifies understanding and reveal misunderstanding
• Supports robust learning by activating prior knowledge and boosting memory
• Supports deeper reasoning• Develops language for expressing
mathematical ideas• Supports development of social
skills• Gives opportunities to learn from
other perspectives
https://store.mathsolutions.com/pub/media/documents/doc/WhyUseTalkinMath_CRD_FG.pdf
In what ways did talk help you as a learner in this parallelogram task?
How might your learning differ if you were instead presented with a lecture about parallelograms?
Principles for Improving the Quality of Discourse in Mathematics Classrooms
Talk moves that engage students in discourse
1
Purposeful questioning
2
Using student thinking to propel discussions3
Setting up a supportive environment
Orchestrating the discourse
5
4
Chapin, O’Connor and Anderson 2009: Classroom Discussion: Using Math Talk to Help Students Learn
Setting up a supportive environment1
“Discourse that focuses on tasks that promote reasoning and problem solving is a primary mechanism for developing conceptual understanding and meaningful learning of mathematics.” p 30
See fig 11, p 31Levels of Classroom Discourse
16
Orchestrating the discourse
“Although discourse provides important opportunities for students to learn what mathematics is and how one does it, creating a culture of discourse in the mathematics classroom also presents challenges… Class discussions can easily become little more than elaborate show and tell sessionsin which it is not clear what each solution adds to students’ developing understanding or how it advances the mathematical storyline of the lesson.” p. 30
Read Illustration on pages 31 - 34 to see how Mr. Donnelly uses these strategies to orchestrate the discussion for learning.Use the chart on page 35 to identify teacher actions he used to facilitate discourse in his classroom.Discuss the implications for teacher professional development. What knowledge and skills will teachers need to use this approach?
2
To orchestrate the discussion (p 30)
1. Anticipate student responses before the lesson2. Monitor students’ work on and engagement with the tasks3. Select particular students to present their work4. Sequence students’ responses in a specific order for discussion5. Connect different students’ responses and connect responses to key ideas
https://www.youcubed.org/resources/stanford-onlines-learn-math-teachers-parents-number-talks/
Using student thinking to propel discussions3
Number Talks
Solve the equation “What is 18 x 5?” without using paper and without using an algorithm.Share your strategy with your group. Have the person to your right re-cap what you’ve shared or compare your strategy to someone else’s.
DiscussIn what ways does this approach advance the mathematical learning of the whole class?
http://tinyurl.com/dxjn8yv
Improving Participation with Talk Moves:
• Re-voicing• Repeating• Reasoning• Adding On• Waiting
4 Talk moves that engage students in discourse
DiscussIn what ways does this approach engage learners more fully in mathematical learning?
Purposeful questioning5
The roles of questions in the math classroom:
• To help students work together to make sense of the mathematics
• To elicit, engage, and challenge student thinking
• To help students rely more on themselves to determine whether something is mathematically correct
Purposeful questioning5 Purposeful Questioning – we ask questions to…
Gg
• Gather information
• Probe thinking
• Make mathematics visible
• Encourage justification and reflection
5
17
Purposeful questioning – Questioning Patterns5
IRE Initiate-response-evaluate
• Review student task on p. 38
• Read excerpts from the whole class discussion, illustrating questioning patternsof funneling and focusing, fig 16, pp. 39-40
• Discuss the results of each questioning pattern in terms of student understanding
• Discuss the implications for professional development around the teacher actions in the chart on page 41. What knowledge and skills will teachers need to use this approach?
Purposeful questioning – Questioning Patterns5
Outline then analyze Principle 4 For more on and purposeful questioning…
HANDOUT 1.11On our web site…
Wrap Up – Day 2Outcomes and Objectives
1. Review work from day 1
2. Review, outline and analyze Wisconsin’s Guiding Principles 1-4 for Teaching and Learning Mathematics
Homework
Be prepared to share in session 3
To review and reinforce: • Pick one area of focus from today.• Read / re-read to learn more about that focus area in your
Principles to Actions book AND• Share new learning about that focus area with someone not
attending this workshop
To prep for day 3: • Complete Mathematics Learning Autobiography
Equity and Access, Depth of Knowledge, Productive Struggle,
Formative Assessment, Discourse, Questioning
18
• Investigate and outline
principles 5 and 6
• Set priorities to address data
• Action plan
Day 3 - Preview What to Bring on Day 3
1. Time allocations for your K-12 universal mathematics instruction
2. Your district mathematics instructional framework (e.g., unit planner, lesson planner)
3. Your homework
4. YOUR POSTERS!!
Stay connected, join the conversation
@WisconsinRtICenter
@WisRtICenter
Tips to Your Inbox: http://bit.ly/WisRtICenter
@Wisconsin RtI Center/PBIS Network
Live webinars and networking events
The Wisconsin RtI Center/Wisconsin PBIS Network (CFDA #84.027) acknowledges the support of the Wisconsin Department of Public Instruction in the development of this presentation and for the continued support of this federally-funded grant program. There are no copyright restrictions on this document; however, please credit the Wisconsin DPI and support of federal funds when copying all or part of this material.
Thank you!
